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A271733
Number of set partitions of [n] with maximal block length multiplicity equal to four.
2
1, 0, 15, 35, 385, 2331, 13335, 88110, 629200, 4811235, 35992957, 276332420, 2325570065, 20036259075, 171879027000, 1583318184855, 14476456463826, 139849724906591, 1347082690705367, 13909222770509990, 144001190692525628, 1519193757875044900
OFFSET
4,3
COMMENTS
At least one block length occurs exactly 4 times, and all block lengths occur at most 4 times.
LINKS
MAPLE
with(combinat):
b:= proc(n, i, k) option remember; `if`(n=0, 1,
`if`(i<1, 0, add(multinomial(n, n-i*j, i$j)
*b(n-i*j, i-1, k)/j!, j=0..min(k, n/i))))
end:
a:= n-> b(n$2, 4)-b(n$2, 3):
seq(a(n), n=4..30);
MATHEMATICA
multinomial[n_, k_List] := n!/Times @@ (k!);
b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 1, 0, Sum[multinomial[n, Join[{n - i*j}, Table[i, j]]]*b[n - i*j, i - 1, k]/j!, {j, 0, Min[k, n/i] }]]];
a[n_] := b[n, n, 4] - b[n, n, 3];
Table[a[n], {n, 4, 30}] (* Jean-François Alcover, May 08 2018, after Alois P. Heinz *)
CROSSREFS
Column k=4 of A271423.
Sequence in context: A219689 A074891 A328213 * A280883 A306325 A241282
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Apr 13 2016
STATUS
approved